The geometry of the mesh gets distorted when rigged and posed
So to fix your problem:

Disable the Multiresolution modifier, because it makes your computer lag (before parenting you need to bake the multires normals so that you can use a low-poly object instead).
Apply the object scale with CtrlA &gt; Scale (explanation about object scale here).
In Edit mode select all and press ShiftN to recalculate the normals.

To avoid parenting bugs it's always better to apply scale and rotation and to make sure that the normals are correctly flipped.
The file is here.